Question

Tgx+3ctgx=4 Решить через " Пусть" Помогите )

Answer 1

Решение во вложении ниже

Answer 2

Problem Statement

The equation to solve is Tgx + 3ctgx = 4. We will solve it using the given approach: "Let's assume".

Solution

Let's assume that Tgx = a. Then, ctgx = 1/tgx = 1/a.

Substituting these values into the equation, we get a + 3(1/a) = 4.

Multiplying through by a to eliminate the denominator, we have a^2 + 3 = 4a.

Rearranging the equation, we get a^2 - 4a + 3 = 0.

Factoring the quadratic equation, we have (a - 3)(a - 1) = 0.

Therefore, a = 3 or a = 1.

Now, let's solve for Tgx and ctgx using these values of a.

For a = 3, we have Tgx = 3 and ctgx = 1/3.

For a = 1, we have Tgx = 1 and ctgx = 1.

Therefore, the solutions to the equation Tgx + 3ctgx = 4 are:

1. Tgx = 3 and ctgx = 1/3. 2. Tgx = 1 and ctgx = 1.

Please note that the solutions are approximate and may require further simplification or verification.